suppose a piece of dust finds itself on a cd. if the spin rate of the cd is 395 rpm, and the piece of dust…

suppose a piece of dust finds itself on a cd. if the spin rate of the cd is 395 rpm, and the piece of dust is 4.0 cm from the center, what is the total distance (in m) traveled by the dust in 8 minutes? (ignore accelerations due to getting the cd rotating.)

suppose a piece of dust finds itself on a cd. if the spin rate of the cd is 395 rpm, and the piece of dust is 4.0 cm from the center, what is the total distance (in m) traveled by the dust in 8 minutes? (ignore accelerations due to getting the cd rotating.)

Answer

Explanation:

Step1: Convert radius from cm to m

The radius (r = 4.0\space cm=0.04\space m)

Step2: Convert rotational speed from rpm to rotations per minute

The rotational speed (n = 395\space rpm) (rotations per minute)

Step3: Calculate the circumference of the circular path

The circumference of a circle is (C = 2\pi r). Substituting (r = 0.04\space m), we get (C=2\pi\times0.04=\frac{2\times22\times0.04}{7}\approx0.251\space m) (using (\pi=\frac{22}{7}))

Step4: Calculate the number of rotations in 8 minutes

The number of rotations (N=n\times t), where (t = 8\space min). So (N=395\times8 = 3160) rotations

Step5: Calculate the total distance

The total distance (d=N\times C). Substituting (N = 3160) and (C\approx0.251\space m), we get (d=3160\times0.251\approx793\space m)

Answer:

(793\space m)